Topological Order, Dimerization, and Spinon Deconfinement in Frustrated Spin Ladders

We consider topological order and dimer order in several frustrated spin ladder models, which are related to higher dimensional models of current interest; we also address the occurrence of fractionalized phases with deconfined spinon excitations in these models. Combining results obtained with both analytic and numerical methods, we discuss how the occurrence of dimerized or fractionalized phases are dictated by the system's geometry.